For #1 theoretically yes they could likely also censor results. This would mean they modified/forked searxng to do so since as far as I know there is no “feature” implemented that lets the admin modify search results beyond configuring which search engines are queried.

For #2 I’m not sure what oracle’s free tier looks like but I guess if it’s free you could give it a shot. I’d say you probably want a VM with at least 1GB of ram and then limit the searxng container to 512MB of ram in docker. 1GB might be tight with the other services that run with it like redis and a reverse proxy like Caddy or NGINX, but could probably be done. I’m using a 2 core 4GB RAM instance and it has plenty of headroom that allows me to self host other small services.This small implementation is obviously sized to be used on a small scale that maybe you and your family and friends use privately, a more public instance would obviously require more resources.